AbstractA pseudo‐transient (static) linear, geometric, material and combined geometric and material non‐linear analyses of composite laminates are presented. A nine‐noded isoparametric quadrilateral finite element belonging to the Lagrangiar family is used in space discretization. An explicit time marching scheme is employed for time integration of the resulting discrete ordinary differential equations with the special forms of diagonal fictitious mass and/or damping matrices. Elasto‐plastic material behaviour is incorporated using the flow theory of plasticity. In particular, a modified version of Hill's initial yield criterion is used in which anisotropy parameters of plasticity are introduced. The shear deformation is accounted for by assuming a constant transverse shear strain across the thickness of the laminate and the geometric non‐linearity is considered in the sense of von Karman strains. The layered element approach is adopted for the treatment of plastic behaviour through the thickness. A wide range of numerical examples is presented to demonstrate the validity and efficiency of the present approach. The results for combined non‐linearity are also presented. The variety of results presented here, which are based on realistic material properties of often‐used advanced laminated composite plates, and especially those for combined non‐linear analysis, should serve as a reference for future